1. Since inflation has been rising since the beginning of 2011, we must be above the natural rate of output (if indeed there is a natural rate of output).

2. The Modigliani-Miller theorem says that changes in the Fed's portfolio of assets (and, hence, QE) must have no effect.

3. Actually I can't understand the third argument at all. This doesn't necessarily mean that Steve's writing is akin to that of William Faulkner on bath salts; instead, it probably reflects my poor reading comprehension.

I actually am not quite sure what to think about the first argument, so I won't address it here. And I don't get what the third argument even is (sorry!). So I'll discuss the second argument: the idea that QE is rendered powerless by the Modigliani-Miller Theorem. Steve writes:

Another useful piece of finance is the Modigliani Miller theorem. Kimball might want to explain to us why, if the Fed issues reserves (overnight liabilities), and buys some other assets, and private financial intermediaries are perfectly capable of issuing overnight liabilities and buying the same assets, that the Fed's QE is not undone.

Now, Steve is not talking about the actual Modigliani-Miller theorem, which says that it doesn't matter whether a company finances itself by issuing bonds or issuing stock. Instead, he's talking about a Modigliani-Miller type result, that says that the government's portfolio is irrelevant.

The archetypical result of this type is Wallace (1981), which you can read here. Under certain highly restrictive and odd-sounding conditions, the government's asset portfolio does not affect the economy at all. One of these conditions, for example, is that the government uses lump-sum taxes to cancel out any net interest payments that it pays to, or receives from, the private sector. If that sounds weird, it's because nothing like that ever happens in the real world. Wallace, of course, freely admits this, and says his model is only intended as a benchmark.

But what if Wallace's model were really in effect? First, realize that it wouldn't just make QE ineffective, it would make Open Market Operations (i.e. the normal thing the Fed does to change interest rates when interest rates are not zero) ineffective as well. For this reason, Jim Bullard of the St. Louis Fed dismisses the Modigliani-Miller type argument. Most people think Open Market Operations really can affect GDP, such as when Paul Volcker reduced the monetary base in the early 80s.

But here's an even more important fact about the Wallace (1981) result: If this result holds, then printing money not only can't effect GDP, it can't affect inflation either. Yep. You read that right. The Modigliani-Miller type result implies that you can print as much money as you want, and prices will stay exactly the same. To quote Wallace:

Irrelevance here means that both the equilibrium consumption allocation and the path of the price level are independent of the path of the government's portfolio. (emphasis mine)

There are some other models similar to Wallace's that yield Modigliani-Miller type results, but they all have this same property.

I doubt that Steve Williamson believes that printing money can't cause inflation. In particular, this post of his from March warns that the excess reserves created by the Fed will create inflation. But if Steve is right about that, then there is no Modigliani-Miller result for QE, and this criticism of Miles Kimball's model is invalid.

Anyway, Steve should take up this argument with St. Louis Fed president Jim Bullard, who has argued forcefully that QE2, the last round of quantitative easing, had some of the effects that it couldn't have in a Wallace (1981) type model. Steve is a big Bullard fan, and will doubtlessly respect his thoughts more than that of a humble graduate student like yours truly...

Update: Miles Kimball responds. The upshot: It might take trillions and trillions of dollars of Fed asset purchases to have an effect on the real economy.

Update 2: Steve Williamson responds, explaining his reasons for believing in a Modigliani-Miller type irrelevance result for QE. He also adds a couple of criticisms of Miles' arguments at the end, but I don't understand these last points, so I can't really comment.

31 comments:

i find it ironic that SW says there is no Phillips curve then whips out inflation to prove we are at full employment.

hang on let me get this straight: there is no phillips curve because wages (prices) are set based on inflation expectations. so the Fed can't create inflation by getting on the loudspeaker "ATTENTION PLEASE 10% INFLATION OF THE MONEY SUPPLY COMING TO A BANK NEAR YOU, WE HAVE 4 GAZILLION BERNANKE BILLS AT THE READY." even if the output gap was huge?

i am so confused, he said sometimes expectations are self fulfilling sometimes not. how do i know which time, do i really want to bet this is the time and not hurriedly spend my money before prices jump?

no wonder were in such a policy trap. seems like half the macro people dont undetstand their own models.

Aren't you an assistant prof now ? Or only in September. I haven't read the Wallace paper, but clearly it doesn't have a cash in advance constraint or money in the utility function or decentralized markets or, you know, any role for money except as a store of value. As such it is not at all relevant to the 80s. But this aspect doesn't make it irrelevant now at the zero lower bound in a liquidity trap.

The paper seems to me to be just a statement of Ricardian equivalence -- in particular the claim seems to be that the Fed can't bear risk removing it from private sector portfolios

because Fed losses imply higher taxes. I'd agree that the direct effects of QE are zero if there is Ricardian equivalence so lump sum tax cuts don't stimulate demand. We don't really have such overwhelming evidence that tax cuts stimulate demand as we have that government spending cuts stimulate demand. I rate Ricardian equivalence like believing in locally realistic models with hidden

i looked at this paper SW posted, and "irrelevance" is violated when there is a legal minimum reserve requirement and storage subsidies (aka interest on reserves). Is it better to have no model, or rely on a silly model? Sometimes no model is better than a silly one.

Yes, it is a bit silly, eh? My point was that if you don't think this model is silly, you think that the Fed can't cause inflation...which is something Steve Williamson does not appear to believe (and does not appear to want to believe, either!)

Steve basically wants to believe in a world where the LRAS curve is vertical, so that printing money causes inflation but doesn't change output. This is a world in which hard money is always good. But Modigliani-Miller type arguments will not get him to such a world.

How can inflation not change output? It reduces the real value of most bonds, transfers wealth from creditors to borrowers, etc. What if the inflation is anticipated? Two points: 1) there are a multitude of (inconsistent) expectations regarding inflation; and 2) it's worth going back to Frank Hahn's work on money and macro. He describes a lot of models in which policy can make things happen even if it's anticipated. (Hahn also shows that many monetarist models gloss over the adjustment problems involved in reaching an equilibrium.)

sorry to report i partly agree with SW, at least on one count: QE might have little effect through the standard "hot potato" money multiplier channel (thats actually the idea of the IOR policy). Demand for excess reserves is perfectly elastic when supply is sufficiently large as IOR functions as a price floor. more or less. IF he's saying QE will just sit as excess reserves he might be correct.

thats a feature not a bug. QE still has *other* effects. The idea of IOR policy is to mitigate the hyperinflationary effects of printing money but still allow the other effects.

The Fed does not print money. It adds reserves to the banking system. Depending on whether those reserves are actually demanded, they might become "money". So I don't see how engaging in QE or OMO alone must result in inflation (aren't $1.3tr in ER's evidence of this?).

I think Williamson is addressing the "portfolio balances" claim. That claim holds that changes in the Fed's portfolio -- whether reserves are demanded or not -- somehow must lead to growth-inducing adjustments in private sector portfolios. The Fed is just another bank, Williamson holds. To claim the Fed has some special ability to induce growth, you have to show how changes to its balance sheet operate differently from private balance sheet changes. For instance, when the Fed supplies demanded bank reserves (see above).

Think about it this way: risk is composed of liquidity, duration and cashflow volatility (credit, earnings) risks. The Fed cannot extinguish duration and cash flow volatility risks; it can only pass them on to taxpayers. The Fed can extinguish liquidity risk by virtue of its irredeemable deposit base; so the Fed does add value in a specific LOLR function. I don't think that is what QE proponents are suggesting.

BTW, as long as ER's exist, QE is not only no different from private bank actions; it is also no different from fiscal policy. Treasury can swap T-bills for risk assets. This is functionally the same as swapping ER's for risk assets to be held in a sovereign wealth fund. Therefore, in this instance, how would the central bank add value through QE?

"1. Since inflation has been rising since the beginning of 2011, we must be above the natural rate of output (if indeed there is a natural rate of output)."

No, I'm not saying that. According to Kimball's logic, if we're above the natural rate then core inflation must be rising. Since core inflation has been rising, therefore Kimball seems to be telling us that we are above the natural rate. Doesn't make any sense, right?

"Instead, he's talking about a Modigliani-Miller type result, that says that the government's portfolio is irrelevant."

Exactly. In this case it doesn't require the special conditions that Wallace needs in his paper (essentially holding fiscal policy constant). All you need is the large quantity of excess reserves (no transactions role for reserves at the margin), and the interest rate on reserves essentially determining the split of outside money between reserves and currency. It's a liquidity trap, but a deeper trap than just a traditional currency shortage.

"Anyway, Steve should take up this argument with St. Louis Fed president Jim Bullard..."

It's funny when macroeconomists invoke Modigliani-Miller, since it's been decisively empirically refuted in the financial economics literature. The main function it serves is as a modus tollens: MM follows from these assumptions, and it doesn't hold, therefore one of these assumptions is wrong.

According to Kimball's logic, if we're above the natural rate then core inflation must be rising. Since core inflation has been rising, therefore Kimball seems to be telling us that we are above the natural rate. Doesn't make any sense, right?

Well, I do wonder about that? Not sure if that "if" is an "if and only if"; as in, I'm not sure if rising inflation means we must be above the natural rate. But I share your puzzlement, so I'll wait for Miles to respond.

In this case it doesn't require the special conditions that Wallace needs in his paper (essentially holding fiscal policy constant). All you need is the large quantity of excess reserves (no transactions role for reserves at the margin), and the interest rate on reserves essentially determining the split of outside money between reserves and currency.

OK. I've never seen a paper that obtains that sort of result...then again the only MM-type result for monetary policy that I've ever really read was Wallace. So do you have a link? I have to see how plausible I think this is.

I'm also not sure that this result is so obvious that it follows just from saying "Modigliani-Miller". If there is an irrelevance result here, it seems subtle and not well-known.

"All you need is the large quantity of excess reserves (no transactions role for reserves at the margin), and the interest rate on reserves essentially determining the split of outside money between reserves and currency. It's a liquidity trap, but a deeper trap than just a traditional currency shortage."

Steve, you've talked about how the Fed is powerless because they can't cut the interest rate on reserves, as they're at about zero, but if they could create more inflation, then that would cut the real rate on reserves.

If the Fed just keeps printing trillions after trillions and keeps buying assets -- at what ever price -- eventually people will have enough money in their bank accounts that they feel comfortable spending, eventually enough trillions will do this. Why not create more inflation then?

Also Steve, if these liquidity traps are so ugly, harmful, and hard to get out of, isn't prevention called for, like not living dangerously with Fed inflation targets so close to zero? Should the normal target be more like 4 or 5 percent?

"Well, I do wonder about that? Not sure if that "if" is an "if and only if"; as in, I'm not sure if rising inflation means we must be above the natural rate. But I share your puzzlement, so I'll wait for Miles to respond."

why do we think we know what the shape of the phillips curve is (except in the long run, its vertical)? The expectations augmented Phillips curve basically says wages are sticky but set based on expected inflation. So, any level of inflation is consistent with any output gap (we learned that in the 70s), particularly with wages downwardly rigid. There is one population (employed, like me) whose annual wage increases are a function of expected inflation (and productivity etc.) and a different population stuck at zero (see figure 2). The average is still positive. In a NK model where wages sticky but still set based on expected future inflation, that is the result you get. That's one of the reasons in a Woodford or NK model, announcing a "future boom" works.

The idea is that the price level is purely passive right now, given a fixed interest rate on reserves. If the private sector creates more liquid assets that compete with reserves, then you get more inflation. If the demand for US-dollar-denominated safe assets goes up in the world, then we get less. But the Fed can't change the inflation rate without changing the interest rate on reserves.

So, the only channel by which issuing more reserves might cause higher inflation is by inducing the private sector to create more liquid assets of its own. So if the private sector does that, will GDP go up, or won't it?

It seems like there has to be a way for the Fed to create inflation if it REALLY wanted to, just don't stop buying debt, even risky private debt, and don't stop until there's inflation. At SOME point, even if you buy it all and then start issuing zero interest loans, at SOME point people will have enough dollars stored away that they start to feel confident spending them.

"But the Fed can't change the inflation rate without changing the interest rate on reserves."

All the Fed has to do is announce a higher inflation target (or NGDP target). Since IOR is a policy choice, whether we get a new higher level of inflation then is a function of credibility of the new target. If the Fed is unwilling to do everything at its disposal (including adjusting IOR), then no, the Fed will not succeed. But as PK and Sumner suggested many many times, the problem right now is that the Fed has too much credibility and has shown itself allergic to even the slightest uptick in inflation.

This seems relatively uncomplicated. The Fed is a bank that happens to have a monopoly on the issuance of dollar bank reserves. At a 25bp (15bp efffective) IOR demand for a marginal dollar of bank reserves is zero. Therefore, from the perspective of changes in its balance sheet alone, the Fed is just a bank.

At the ZLB, arguments around Ricardian equivalence also apply to QE-equivalent fiscal actions (i.e. Treasury swapping T-bills for risk assets). Therefore the "portfolio balances" effect, if it exists, is just fiscal policy in disguise.

A negative IOR or signaling effect is just the case of the Fed attempting to move us away from zero demand for bank reserves. In a liquidity trap, you can argue "QE works if signaling succeeds", but not "QE works in any circumstance".

As always, I find this very interesting, and generally clear. I admit to having some trouble with the Modigliani-Miller theorem, since whenever I read that coupling I keep visualizing the Tropic of Cancer profusely illustrated by odd-looking nudes, but I suspect that sooner or later I'll get past that. At any rate, I sympathize with dwb's point on models. Models, in my experience, are rather like experts - the great danger of being an expert is that you start to think you know what you're talking about. Similarly, the great danger of models is that you start to believe that they accurately reflect reality. There may be some models which reflect reality well enough, but most models I ever encountered in my area of less-than-expertise were at best, rather crude approximations of the world. Most of us at that time tried hard to avoid the trap of thinking of them as anything but a source of insight and perhaps inspiration, but it may be the case that Economics now is a much more mature science than ecology was then. I would certainly not know that myself.